Adaptive coefficient signal generator for adaptive signal equalizers with fractionally-spaced feedback

ABSTRACT

An adaptive coefficient signal generator for use in an adaptive signal equalizer with fractionally-spaced feedback. The signals representing the feedback tap coefficients are generated in conjunction with a timing interpolation parameter such that the fractionally-spaced feedback circuitry dynamically emulates symbol-spaced feedback circuitry.

RELATED APPLICATIONS

This is a continuation-in-part of U.S. patent application Ser. No. 10/290,571, filed Nov. 8, 2002.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to signal transmission and detection, and in particular, to techniques for compensating for signal distortions caused by signal dispersion and nonlinearities within the signal transmission media.

2. Description of the Related Art

Signal processing architectures for intersymbol interference (ISI) equalization as used for communications transmission and/or storage systems may be divided into two categories: discrete-time architecture and continuous-time architecture. Discrete-time architectures, commonly used in current systems, use a sampled approach to render the input continuous-time, analog waveform in discrete form. Typically, a high resolution A/D converter, which follows the analog anti-aliasing filter, is used as the sampler at the analog front end. Continuous-time architectures use an analog continuous-time approach which directly processes and equalizes the incoming analog waveform while remaining in the continuous time domain until the final data bit stream is generated.

At present, those signal processing architectures having a feedforward transversal filter and a feedback filter as their basic components are considered, and in particular, the following scenarios: discrete-time/continuous-time architectures with fractionally-spaced (i.e., tap spacing less than symbol-spaced) feedforward taps; continuous-time architecture with feedback that is nominally symbol-spaced; continuous-time/discrete-time architectures with fractionally-spaced feedback. For purposes of the presently claimed invention, the following discussion concerns “fat tap” adaptation to cover the continuous-time architecture with fractionally-spaced feedback; however, such discussion may be readily extended to cover the other scenarios as well.

Fractional-spaced feedforward filters have commonly been used either as stand-alone linear equalizers or in combination with Decision Feedback. Advantages of fractional-spaced versus symbol-spaced feedforward filters include: added robustness to constant or slowly varying sampling phase offset or sampling jitter; and improved signal-to-noise ratio (SNR) sensitivity, particularly in the absence of complete channel information, due to the role of the fractional-spaced filter as a combined adaptive matched filter and equalizer.

The adaptation technique for the tap coefficients have always implicitly assumed independence in the adaptation of the successive tap coefficients, which has been based on minimizing the mean squared error (MSE) as computed using the difference between the slicer input and output. This adaptation technique is referred to as LMSE (least mean squared error) or MMSE (minimized mean squared error) adaptation. It can be shown that the LMSE adaptation for both fractional feedforward or symbol spaced feedback at iteration k+1 reduces to the following coefficient update equations: c ^((k+1)) =c ^((k)) +μe ^((k)) s(discrete-time adaptation case) where c ^((k)) is the tap coefficient vector and e^((k)) the corresponding error at the k^(th) iteration, s is the vector with components as the input waveform to the corresponding tap mixer and μ is a constant and is an adaptation parameter; and

$\underset{\_}{c} = {\int_{0}^{t}{{\mu \cdot {e(t)}}{\underset{\_}{s}(t)}{\mathbb{d}t}\mspace{14mu}\left( {{continuous}\text{-}{time}\mspace{14mu}{adaptation}\mspace{14mu}{case}} \right)}}$ with similar terminology as above.

When continuous-time feedback is considered, a number of difficulties are encountered. For example, it is difficult and sometimes unfeasible to design precisely symbol-spaced, flat group delay filters. If the total group delay on the feedback path for canceling successive past symbols is even slightly different from the corresponding symbol period, the performance loss can be substantial. This may necessitate the need for using fractionally-spaced feedback filters. Fractionally-spaced feedback filters may also be needed to account for the slicer-induced jitter and/or the data bits pattern-specific group delays due to frequency dependent group delays of the slicer, mixer and any other analog/digital component on the feedback data path. Further when an equalizer with fractionally-spaced feedback taps is used, independent LMS adaptation of the successive feedback taps fails because of the strongly correlated nature of the fractional tap-spaced feedback data.

SUMMARY OF THE INVENTION

In accordance with the presently claimed invention, an adaptive coefficient signal generator for use in an adaptive signal equalizer with fractionally-spaced feedback generates signals representing feedback tap coefficients in conjunction with a timing interpolation parameter such that the fractionally-spaced feedback circuitry dynamically emulates symbol-spaced feedback circuitry. Advantages realized with the presently claimed invention include avoidance of a need for precisely symbol-spaced flat group delay filters, and the ability to account for slicer-induced jitter as well as variable group delays specific to certain data bit patterns due to frequency dependent group delays of various system elements (e.g., slicer(s) and mixer(s) in the feedback data path).

As will become evident from the following discussion, the presently claimed invention can be implemented and practiced in either the continuous time (e.g., analog) or discrete time (e.g., digital) domain. At the present point in time, data symbol rates less than one gigabit per second (1 Gb/s) can often be processed in either the continuous or discrete time domain, while data symbol rates greater than 1 Gb/s must generally be processed in the continuous time domain. However, as the applicable technology advances, it is expected that data symbol rates in excess of 1 Gb/s will also become more susceptible to processing in the discrete time domain as well. As will become further evident, the presently claimed invention benefits the host system or network by effectively increasing the signal-to-noise ratio (SNR), thereby reducing the bit error rate (BER) and, in turn, adding robustness (e.g., with respect to phase offsets or jitter among the data symbols). For example, in the case of a fiber optic network, such added performance and robustness will allow a longer network to be realized without a concomitant increase in network infrastructure.

In accordance with one embodiment of the presently claimed invention, an adaptive feedback coefficient signal generator for use in an adaptive signal equalizer with an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, with fractionally-spaced feedback and in which an equalization feedback signal adaptively equalizes an incoming data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal includes signal multiplication circuitry, signal combining circuitry, signal integration circuitry, signal weighting circuitry and signal complement circuitry. First signal multiplication circuitry receives and multiplies a plurality of multiplicand signals to provide a plurality of product signals. The plurality of multiplicand signals includes: a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith; a second data signal corresponding to the first data signal and delayed by a fraction of the data symbol period; an error signal corresponding to a difference between the post-slicer data signal and a pre-slicer data signal; a first adaptation control signal having a first value bounded by lower and upper values; and a second adaptation control signal having a second value related to a difference between a normalized value and the first value. The plurality of product signals includes: a first product signal corresponding to a product of the first data signal, the error signal and the first adaptation control signal; and a second product signal corresponding to a product of the second data signal, the error signal and the second adaptation control signal. The signal combining circuitry, coupled to the first signal multiplication circuitry, receives and combines the plurality of product signals to provide a combined signal. The signal integration circuitry, coupled to the signal combining circuitry, receives and integrates the combined signal to provide a third adaptation control signal. Second signal multiplication circuitry, coupled to the signal integration circuitry, receives and multiplies the first, second and third adaptation control signals to provide a plurality of adaptive feedback coefficient signals. The signal weighting circuitry, coupled to the first signal multiplication circuitry and the second signal multiplication circuitry, receives a plurality of weighted coefficient signals and in response thereto receives and weights a plurality of adaptive filter coefficient signals to provide the first adaptation control signal. The signal complement circuitry, coupled to the first signal multiplication circuitry, the second signal multiplication circuitry and the signal weighting circuitry, receives and complements the first adaptation control signal to provide the second adaptation control signal.

In accordance with another embodiment of the presently claimed invention, an adaptive feedback coefficient signal generator for use in an adaptive signal equalizer with an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, with fractionally-spaced feedback and in which an equalization feedback signal adaptively equalizes an incoming data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal includes first and second control signal generator circuitry. The first control signal generator circuitry receives and processes a plurality of input signals and first and second adaptation control signals and in response thereto provides a plurality of adaptive feedback coefficient signals. The plurality of input signals includes: a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith; a second data signal corresponding to the first data signal and delayed by a fraction of the data symbol period; and an error signal corresponding to a difference between the post-slicer data signal and a pre-slicer data signal. The second control signal generator circuitry, coupled to the first control signal generator circuitry, receives and processes a plurality of adaptive filter coefficient signals and in response thereto provides the first and second adaptation control signals.

In accordance with another embodiment of the presently claimed invention, a method for generating adaptive feedback coefficient signals for adaptive signal equalization using an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, fractionally-spaced feedback and an equalization feedback signal to generate an adaptively equalized data signal as a pre-slicer data signal that is sliced to provide a post-slicer data signal includes:

receiving and multiplying a plurality of multiplicand signals to generate a plurality of product signals, wherein

-   -   the plurality of multiplicand signals includes         -   a first data signal corresponding to a post-slicer data             signal and having a data symbol period associated therewith,         -   a second data signal corresponding to the first data signal             and delayed by a fraction of the data symbol period,         -   an error signal corresponding to a difference between the             post-slicer data signal and a pre-slicer data signal,         -   a first adaptation control signal having a first value             bounded by lower and upper values, and         -   a second adaptation control signal having a second value             related to a difference between a normalized value and the             first value, and     -   the plurality of product signals includes         -   a first product signal corresponding to a product of the             first data signal, the error signal and the first adaptation             control signal, and         -   a second product signal corresponding to a product of the             second data signal, the error signal and the second             adaptation control signal;

combining the plurality of product signals to generate a first combined signal;

integrating the first combined signal to generate a third adaptation control signal;

multiplying the first, second and third adaptation control signals to generate a plurality of adaptive coefficient signals;

receiving a plurality of weighted coefficient signals and in response thereto receiving and weighting a plurality of adaptive filter coefficient signals to generate the first adaptation control signal; and

complementing the first adaptation control signal to generate the second adaptation control signal.

In accordance with another embodiment of the presently claimed invention, a method for generating adaptive feedback coefficient signals for adaptive signal equalization using an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, fractionally-spaced feedback and an equalization feedback signal to generate an adaptively equalized data signal as a pre-slicer data signal that is sliced to provide a post-slicer data signal includes:

receiving and processing a plurality of input signals and first and second adaptation control signals to generate a plurality of adaptive feedback coefficient signals, wherein the plurality of input signals includes

-   -   a first data signal corresponding to a post-slicer data signal         and having a data symbol period associated therewith,     -   a second data signal corresponding to the first data signal and         delayed by a fraction of the data symbol period, and     -   an error signal corresponding to a difference between the         post-slicer data signal and a pre-slicer data signal; and

receiving and processing a plurality of adaptive filter coefficient signals to generate the first and second adaptation control signals.

BRIEF DESCIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of decision feedback equalization (DFE) circuitry in which an adaptive coefficient signal generator in accordance with the presently claimed invention can advantageously provide for improved data signal equalization.

FIG. 2 is a block diagram of the feedback portion of a DFE circuit in which an adaptive coefficient signal generator in accordance with the presently claimed invention is used to provide the adaptive coefficient signals.

FIG. 3 is a block diagram of one embodiment of an adaptive coefficient signal generator in accordance with the presently claimed invention.

FIG. 4 is a block diagram of an exemplary implementation of the adaptive coefficient signal generator of FIG. 3.

FIG. 5 is a block diagram of another embodiment of an adaptive coefficient signal generator in accordance with the presently claimed invention.

FIG. 6 is a block diagram of an exemplary implementation of the adaptive coefficient signal generator of FIG. 5.

FIG. 7 is a block diagram of an alternative implementation of the adaptive coefficient signal generator of FIG. 4.

FIG. 8 is a block diagram of an alternative implementation of the adaptive coefficient signal generator of FIG. 6.

FIG. 9 is a block diagram depicting signal adaptation using correlated taps in accordance with another embodiment of the presently claimed invention.

FIG. 10 is a block diagram of another embodiment of an adaptive coefficient signal generator in accordance with the presently claimed invention.

FIG. 11 is a block diagram of feedforward equalization (FFE) circuitry with which the adaptive coefficient signal generator of FIG. 10 can share adaptive filter coefficient signals.

FIG. 12 is a block diagram of an exemplary implementation of an adaptive filter coefficient signal generator for providing adaptive filter coefficient signals for the adaptive coefficient signal generator of FIG. 10.

FIG. 13 is a block diagram of an exemplary implementation of a portion of the adaptive coefficient signal generator of FIG. 10.

FIG. 14 is a block diagram of an alternative implementation of a portion of the adaptive coefficient signal generator of FIG. 10.

FIG. 15 is a block diagram of an exemplary implementation of the adaptive coefficient signal generator of FIG. 10.

FIGS. 16A and 16B illustrate expected performance improvement with use of an analog continuous-time feedforward filter in conjunction with “fat tap” adaptation in accordance with the presently claimed invention.

DETAILED DESCRIPTION OF THE INVENTION

The following detailed description is of example embodiments of the presently claimed invention with references to the accompanying drawings. Such description is intended to be illustrative and not limiting with respect to the scope of the present invention. Such embodiments are described in sufficient detail to enable one of ordinary skill in the art to practice the subject invention, and it will be understood that other embodiments may be practiced with some variations without departing from the spirit or scope of the subject invention.

Throughout the present disclosure, absent a clear indication to the contrary from the context, it will be understood that individual circuit elements as described may be singular or plural in number. For example, the terms “circuit” and “circuitry” may include either a single component or a plurality of components, which are either active and/or passive and are connected or otherwise coupled together to provide the described function. Additionally, the term “signal” may refer to one or more currents, one or more voltages, or a data signal. Within the drawings, like or related elements will have like or related alpha, numeric or alphanumeric designators. Further, while the present invention has been discussed in the context of implementations using discrete electronic circuitry (preferably in the form of one or more integrated circuit chips), the functions of any part of such circuitry may alternatively be implemented using one or more appropriately programmed processors, depending upon the signal frequencies or data rates to be processed.

The subject matter discussed herein, including the presently claimed invention, is compatible and suitable for use with the subject matter disclosed in the following copending, commonly assigned patent applications (the disclosures of which are incorporated herein by reference): U.S. patent application Ser. No. 10/117,293, filed Apr. 5, 2002, and entitled “Compensation Circuit For Reducing Intersymbol Interference Products Caused By Signal Transmission Via Dispersive Media”; U.S. patent application Ser. No. 10/179,689, filed Jun. 24, 2002, and entitled “Crosstalk Compensation Engine For Reducing Signal Crosstalk Effects Within A Data Signal”; U.S. patent application Ser. No. 10/244,500, filed Sep. 16, 2002, and entitled “Compensation Method For Reducing Intersymbol Interference Products Caused By Signal Transmission Via Dispersive Media”; U.S. patent application Ser. No. 10/290,674, filed Nov. 8, 2002, and entitled “Compensation Circuit And Method For Reducing Intersymbol Interference Products Caused By Signal Transmission Via Dispersive Media”; U.S. patent application Ser. No. 10/290,993, filed Nov. 8, 2002, and entitled “Adaptive Signal Equalizer With Adaptive Error Timing And Precursor/Postcursor Configuration Control”; U.S. patent application Ser. No. 10/321,893, filed Dec. 17, 2002, and entitled “Adaptive Signal Latency Control For Communications Systems Signals”; U.S. patent application Ser. No. 10/321,876, filed Dec. 17, 2002, and entitled “Adaptive Signal Equalizer With Adaptive Error Timing And Precursor/Postcursor Configuration Control”; and U.S. patent application Ser. No. 10/179,996, filed Jun. 24, 2002, and entitled “Programmable Decoding of Codes of Varying Error-Correction Capability”.

In accordance with the presently claimed invention, a group of two or more adjacent fractionally-spaced feedback taps are viewed to be correlated and corresponding to essentially the same symbol so that this group of fractionally-spaced taps essentially emulates a symbol-spaced feedback tap. Such a group of fractionally-spaced taps that emulates a symbol-spaced feedback tap is referred herein as a “fat tap.” Thus, successive fat taps emulate different symbol-spaced feedback taps. The adaptation of the taps within the fat tap should have some kind of adaptive timing interpolation between them so that the effective timing of the fat tap corresponds to the corresponding symbol timing. Further, both taps in the fat tap need to adapt together using LMSE adaptation, for instance, since their inputs are correlated.

The emphasized case will be that in which successive fat taps consist of disjoint taps and, thus, represent independent symbols (e.g., referred to as Independent Fat Tap Adaptation (IFTA)). Also emphasized will be the case with the constraint of only two taps within the fat tap.

Let the feedback tap spacing be denoted by τ which is sufficiently less than the symbol period. It is assumed that the feedback symbol waveform is approximately piece-wise linear within the span of time interval τ. Thus, if the feedback signal is denoted as s(t), the parametric equation of the line passing through s(t) and s(t−τ) may be denoted via: r·s(t)+(1−r)·s(t−τ) for the parameter r (in general, −∞<r<∞). With the piecewise linear assumption of s(t), we have: s(t−τ _(r))≈r·s(t)+(1−r)·s(t−τ) for a suitable choice of the delay τ_(r). Note that with the piecewise linear approximation: τ_(r)≈(1−r)·τ.

With a linear approximation of the feedback signal waveform, we represent the two tap coefficients of the fat tap as c·r and c·(1−r) where the quantity r is the timing interpolation parameter which ideally should achieve effective symbol spaced timing for the fat tap, and the quantity c is used for LMSE adaptation for estimating the past ISI that needs to be cancelled. Thus, with these two parameters, the fat tap tries to emulate the corresponding symbol-spaced feedback tap with LMS tap coefficient c. The correlation ratio between the two adapting taps of the fat tap is then

$\frac{r}{1 - r}.$ It is then required to adapt the parameters c and r for the fat tap.

For the continuous-time case, the LMSE adaptation of the parameters c and r can then be shown to be:

$\begin{matrix} {{\left. {{c(t)} = {\mu_{c} \cdot {\int_{0}^{t}{{e(v)} \cdot \left\lbrack {{r \cdot {s(v)}} + 1 - r} \right) \cdot {s\left( {v - \tau} \right)}}}}} \right\rbrack{\mathbb{d}v}};} \\ {{r(t)} = {\mu_{r} \cdot {\int_{0}^{t}{{{c(v)} \cdot {e(v)} \cdot \left\lbrack {{s(v)} - {s\left( {v - \tau} \right)}} \right\rbrack}{\mathbb{d}v}}}}} \end{matrix}$ If, as may be typical, sign(c)=−1, and since

${{{s(v)} - {s\left( {v - \tau} \right)}} \approx {k\frac{\mathbb{d}\;}{\mathbb{d}t}{s\left( {v - \tau_{r}} \right)}}},$ for a constant k, the update equation for r(t) may also be simplified to:

${r(t)} = {{- \mu_{r}^{1}} \cdot {\int_{0}^{t}{{{e(v)} \cdot \frac{\mathbb{d}\;}{\mathbb{d}v}}{s\left( {v - \tau_{r}} \right)}{{\mathbb{d}v}.}}}}$ Note that

$\frac{\mathbb{d}\;}{\mathbb{d}t}{s\left( {t - \tau_{r}} \right)}$ may easily be implemented by passing the output of the fat tap through a C-R differentiator block, which is a high-pass filter.

For the discrete-time case, the LMSE adaptation of the parameters c and r can then be shown to be: c ^((k+1)) =c ^((k))+μ_(c) ·e ^((k)·[) r ^((k)) ·s(t)+(1−r ^((k)))·s(t−τ)] r ^((k+1)) =r ^((k))+μ_(r) ·c ^((k)) ·e ^((k)·[) s(t)−s(t−τ)] The update equation for r can also be simplified to (if its known that sign(c)=−1): r ^((k+1)) =r ^((k))−μ_(r) ·e ^((k)·[) s(t)−s(t−τ)]

The next step is determining which pair of two (or more) taps belong to the same fat tap. The specific two adjacent taps which form a fat tap corresponding to a specific past symbol may vary depending on the group delay variations of different analog or digital components within the feedback path such as the slicer, delay elements, summer, mixer, etc. One approach is to hypothesize that different (disjoint) pairs of taps correspond to different fat taps corresponding to different past symbols. Then, depending on the values of the feedback tap coefficients after convergence, specifically the timing interpolation parameter which should ideally be within the range (0,1) and/or the hypothesis which corresponds to the minimum mean squared error, the winning hypothesis may be selected as part of the start-up procedures of the circuit. (As noted above, ideally 0<r<1, although in general, −∞<r<∞. However, it should be understood that maximum advantages of timing interpolation as provided by the presently claimed invention are realized when 0<r<1 (e.g., where the complement 1−r of r when r=0.2 is 1−r=1−0.2=0.8). When r lies outside of the range (0,1), i.e., −∞<r<0 or 1<r<∞ (e.g., where the complement 1−r of r when r=1.2 is 1−r=1−1.2=−0.2), extrapolation takes place instead of interpolation and performance degradation may result.

Referring to FIG. 1, a decision feedback equalizer (DFE) 100 typically includes a feed forward filter 102 and a feedback filter 104. The feedback filter 104 processes the decisions d_(k) from the output of the final signal slicer 106. The coefficients, or gains, F*_(i) can be adjusted to cancel ISI on the current symbol based upon past detected symbols. The feed forward filter 102 has N₁+N₂+1 taps while the feedback filter 104 has N₃ taps, and the output {circumflex over (d)}_(k) 109 of the final signal summer 108 can be expressed as follows:

${\hat{d}}_{k} = {{\sum\limits_{n = {- N_{1}}}^{N_{2}}{c_{n}^{*}y_{k - n}}} + {\sum\limits_{i = 1}^{N_{3}}{F_{i}d_{k - i}}}}$ where

-   -   c*_(n)=tap gains for feed forward filter 102     -   y_(n)=input signals to feed forward filter 102     -   F*_(i)=tap gains for feedback filter 104     -   d_(i)(i<k)=previous decision made upon detected signal d_(k)

More specifically, with respect to the feedback filter section 104, the output signal 107 is successively delayed through a sequence of time delay elements 110 a, . . . 110 n (e.g., with each successive time delay element 110 imparting a time delay equal to one symbol). Each of the successively time-delayed signals 111 a, . . . 111 n are processed in their respective adaptive gain stages 112 a, . . . 112 n to provide corresponding adaptive feedback signals 113 a, . . . 113 n which are summed together in a signal summing circuit 114 to produce the equalization feedback signal 115.

The adaptive gain stages 112 a, . . . 112 n process their respective time-delayed signals 111 a, . . . 111 n based upon an error signal 117 representing the error, if any, between the post-slicer data signal 107 and the pre-slicer data signal 109. This error signal 117 is typically generated by subtracting the pre-slicer data signal 109 from the post-slicer data signal 107 in a signal summing circuit 116.

The adaptive gain stages 112 a, 112 b, . . . 112 n process their respective time-delayed signals 111 a, 111 b . . . 111 n based upon an error signal 117 representing the error, if any, between the post-slicer data signal 107 and the pre-slicer data signal 109. This error signal 117 is typically generated by subtracting the pre-slicer data signal 109 from the post-slicer data signal 107 in a signal summing circuit 116.

Referring to FIG. 2, a feedback filter 104 a for use in a DFE in a continuous time signal application includes the time delay elements 110 as well as the adaptive gain stages 112. In accordance with the presently claimed invention, each of the time delay elements 110 is a fractional delay element and, therefore, imparts to its data signal a time delay of a fraction of the data symbol, and each of the adaptive gain stages 112 is a multiplier that multiplies its respective time-delayed input signal 111 by one of two adaptive coefficient signals 205 b, 205 c (discussed in more detail below). Additionally, a fat tap adaptation (FTA) stage 200 is included. As discussed in more detail below, this FTA stage 200 provides the adaptive coefficient signals 205 b, 205 c. In accordance with one embodiment, this FTA stage 200 provides these adaptive coefficient signals 205 b, 205 c in accordance with the error signal 117 and the corresponding time-delayed signal 111 a, 111 b processed by the related adaptive gain stages 112 aa, 112 ba. In accordance with another embodiment, the FTA stage 200 also uses the equalization feedback signal 115.

It should be understood that, in conformance with the discussion herein, additional pairs of adaptive gain stages 112 can also have corresponding FTA stages 200; however, only one such FTA stage 200 is shown in FIG. 2 for purposes of simplified illustration.

By using the adaptive coefficient signals 205 b, 205 c provided by the FTA stage 200, adaptive gain stages 112 aa and 112 ba operate as correlated taps since adaptive coefficient signals 205 b and 205 c are correlated (discussed in more detail below). On the other hand, those among the remaining adaptive gain stages 112 ca, . . . 112 na-1, 112 na that do not use a corresponding FTA stage 200 are independent taps to the extent that their respective adaptive coefficient signals Cca, . . . , Cna-1, Can are independent, i.e., uncorrelated.

Referring to FIG. 3, one example 200 a of the FTA stage 200 (FIG. 2) includes multiplier circuits 202 a, 202 b and control signal generator circuitry implemented as a coefficient signal generator 204 a and a timing interpolation parameter signal generator 206 a, all interconnected substantially as shown. The adjacent time-delayed feedback signals 111 a, 111 b are multiplied in their respective multiplier circuits 202 a, 202 b with the error signal 117. The resulting product signals 203 a, 203 b are processed by the control signal generator circuits 204 a, 206 a. As discussed in more detail below, the first control signal generator circuit 204 a provides an adaptation control signal 205 a to the second control signal generator circuit 206 a which, in return, provides two other adaptation control signals 207 a, 207 b to the first control signal generator 204 a. As a result of processing these input signals 203 a, 203 b, 207 a, 207 b, the first control signal generator circuit 204 a provides the adaptive coefficient signals c(t)r(t) 205 b, c(t)(1−r(t)) 205 c, where signal element c(t) is the weighting factor and signal element r(t) is the factor indicative of the degree of correlation between the adjacent time-delayed feedback signals 111 a, 111 b.

Referring to FIG. 4, one example 200 aa of the FTA circuit 200 a of FIG. 3 implements the control signal generators 204 a, 206 a substantially as shown. In the first control signal generator 204 aa, the initial product signals 203 a, 203 b are further multiplied in further multiplier circuits 212 aa, 212 ba with the adaptation control signals 207 aa, 207 ba from the other control signal generator 206 aa. An additional constant signal 211 can also be multiplied as part of the product operations, or can be implemented as a constant scaling factor within the multiplier circuits 212 aa, 212 ba.

The resulting product signal 213 aa, 213 ba are summed in a signal summing circuit 214. The resulting sum signal 215 is integrated in an integration circuit 216 (e.g., a low pass filter) to produce the first adaptation control signal 205 aa. This adaptation control signal 205 aa, in addition to being provided to the other control signal generator 206 a, is multiplied within further multiplication circuits 218 a, 218 b with the other adaptation control signals 207 aa, 207 ba provided by the other control signal generator 206 aa. The product signals resulting from these multiplication operations are the adaptive coefficient signals 205 ba, 205 ca.

In the second control signal generator 206 aa, the initial product signals 203 a, 203 b are differentially summed in a signal summing circuit 222, where the second product signal 203 b is subtracted from the first product signal 203 a. The resulting difference signal 223 is multiplied in a multiplier circuit 224 a with the adaptation control signal 205 aa provided by the first control signal generator 204 aa. As with the input multiplier circuits 212 aa, 212 ba of the first control signal generator 204 aa, an additional constant signal 221 can also be used in this multiplication operation, or, alternatively, be implemented as a constant scaling factor within the multiplication circuit 224 a operation.

The resulting product signal 225 is integrated by another signal integration circuit 226 (e.g., a low pass filter) to produce one of the adaptation control signals 207 aa used by the first control signal generator 204 aa.

This adaptation control signal 207 aa is further processed by a signal complement circuit 228 in which the input signal 207 aa is subtracted from a reference signal having a normalized value, with the resulting difference signal 207 ba serving as the other adaptation control signal used by the first control signal generator 204 aa. For example, if the value of the incoming signal 207 aa were considered to have a normalized signal value range bounded by the values of zero and unity, the signal complement circuit 228 subtracts the incoming signal 207 aa from the value of unity to produce the output signal 207 ba.

Referring to FIG. 5, another embodiment 200 b of the FTA circuitry 200 (FIG. 2) uses alternative implementations 204 b, 206 b of the control signal generators to process the incoming data signals 111 a, 111 b, the error signal 117 and the equalization feedback signal 115.

Referring to FIG. 6, one implementation 200 ab of the FTA circuit 200 b of FIG. 5 can be implemented substantially as shown. In the first control signal generator 204 ba, the time-delayed data signals 111 a, 111 b and error signal 117 are multiplied in the multiplier circuits 212 ab, 212 bb (with the multiplication, or scaling, constant 211 included as part of the operation as discussed above) along with the adaptation control signals 207 ab, 207 bb from the other control signal generator 206 ba. The resulting product signals 213 ab, 213 bb are summed in the summing circuit 214. The resulting sum signal 215 is integrated in the signal integration circuit 216 (e.g., a low pass filter) to produce an adaptation control signal 205 ab (which, in this implementation, is used internally and is not provided to the other control signal generator 206 ba). This signal 205 ab is multiplied in output multiplier circuits 218 a, 218 b with the adaptation control signals 207 ab, 207 bb provided by the other control signal generator 206 ba to produce the adaptive coefficient signals 205 bb, 205 cb.

In the second control signal generator 206 ba, the equalization feedback signal 115 is differentiated in a signal differentiation circuit 232 (e.g., a high pass filter). The resulting differentiated signal 233 is multiplied in a multiplier circuit 224 b with the error signal 117 (with the multiplication, or scaling, constant 221 included as part of the operation as discussed above). The resulting product signal 207 ab forms one of the adaptation control signals provided to the first control signal generator 204 ba. This signal 207 ab is also complemented by the signal complement circuit 228 (as discussed above) to produce the other adaptation control signal 207 bb provided to the first control signal generator 204 ba.

Referring to FIG. 7, an adaptive coefficient signal generator in accordance with another embodiment 300 of the presently claimed invention includes error mixer stages 302, 304, a complement integrating mixer stage 306, an integrating mixer stage 308 and a complement coefficient mixer stage 312, all interconnected substantially as shown. The time-delayed data signals 111 a, 111 b are received and processed by the error mixer stages 302, 304. Each error mixer stage 302, 304 multiplies these signals 111 a, 111 b with the error signal 117 in signal multipliers 352, 354. The resulting product signals 353, 355 are summed in a signal combiner 356 and the sum signal 357 is integrated by a signal integration circuit 358 (e.g., a low pass filter).

The signals 303, 305 produced by these mixer stages 302, 304 are further processed by the complement integrating mixer stage 306 and integrating mixer stage 308. The complement integrating mixer 306 multiplies signals 303 and 305 in signal multipliers 360, 362 with the signal 309 produced by the integrating mixer stage 308. The resulting product signals 361, 363 are summed in a signal combiner 364. The sum signal 365 is integrated by a signal integration circuit 366 (e.g., a low pass filter).

The integrating mixer stage 308 multiplies signal 303 and signal 305 (which is inverted by a signal inversion circuit 310) in signal multipliers 370, 372 with the signal 307 produced by the complement integrating mixer stage 306. The resulting product signals 371, 373 are summed in a signal combiner 374. The sum signal 375 is integrated by a signal integration circuit 376 (e.g., a low pass filter).

The signals 307, 309 produced by the complement integrating mixer stage 306 and integrating mixer stage 308 are multiplied in the signal multipliers 380, 382 of the complement coefficient mixer stage 312 with the signal 309 produced by the integrating mixer stage 308. The resulting product signals 381, 383 are integrated in respective signal integration circuits 384, 386 (e.g., low pass filters), thereby producing the adaptive coefficient signals 205 bc, 205 cc.

Referring to FIG. 8, an adaptive coefficient signal generator in accordance with another embodiment 240 of the presently claimed invention shares some similarities with the implementation shown in FIG. 6. The data signals 111 a, 111 b are multiplied in multiplier circuits 212 ac, 212 bc (with a multiplication, or scaling, constant 211 as desired). The resulting product signals 213 ac, 213 bc are summed in a signal combiner 214 a and the sum signal 215 a is buffered by a gain stage 214 b. The resulting buffered signal 215 b is multiplied in a signal multiplier 118 with an integrated signal 245 (discussed in more detail below) to produce the equalization feedback signal 115 a, and is also processed by two signal delay stages 246, 248 (discussed in more detail below).

The buffered signal 215 b is processed by the first signal delay stage 246, which compensates for signal delays introduced by the signal slicer 106 (FIG. 1), the feedback signal multiplication circuit 118 and the feedback signal summing circuitry 108 (FIG. 1) while subtracting out a delay corresponding to that introduced by the signal inversion circuitry 250 and signal differentiation circuit 232 a. The delayed signal 247 is inverted in a signal inversion circuit 250. The inverted signal 251 is differentiated in a signal differentiation circuit 232 a (e.g., a high pass filter).

The differentiated signal 233 a is multiplied in a signal multiplier 224 c with the error signal 117 (along with a multiplication, or scaling, constant 221 as desired). The resulting product signal 225 c is integrated in a signal integration circuit 226 a (e.g., a low pass filter) to produce the adaptation control signal 227 a for signal multiplier 212 bc. This signal 227 a is also complemented by a signal complement circuit 228 a (as discussed above) to produce the other adaptation control signal 229 a for signal multiplier 212 ac.

The second signal delay stage 248 compensates for signal delays introduced by the signal slicer 106 (FIG. 1), the feedback multiplier 118 and feedback signal summer 108 (FIG. 1). The resulting delayed signal 249 is multiplied in a signal multiplier 242 with the error signal 117. The resulting product signal 243 is integrated in a signal integration circuit 244 (e.g., a low pass filter). The integrated signal 245 is multiplied with the buffered signal 215 b in the feedback signal multiplier 118 to produce the equalization feedback signal 115 a.

Referring to FIG. 9, the adaptive coefficient signals as discussed above can be used in an adaptive signal equalizer with fractionally-spaced feedback in a number of ways. As discussed above, the time-delayed data signals 111 a, 111 b are multiplied in signal multipliers 112 aa, 112 ba with the adaptive coefficient signals 205 b, 205 c, with the resulting product signals 113 aa, 113 ba combined in a signal combiner 114 a to produce a signal 115 a which may or may not be the final equalization feedback signal (discussed in more detail below). For example, in scenario A, the first adaptation control signal 205 b corresponds to a product of a weighting factor c(t) and the correlation factor r(t), while the second adaptation control signal 205 c corresponds to a product of the weighting factor c(t) and the complement [1−r(t)] of the correlation factor r(t). The sum signal 115 a can be used directly as the final equalization feedback signal or can be further scaled (e.g., multiplied by a value of unity) in the output multiplier 114 b to produce the final equalization feedback signal 115 b.

In scenario B, the first adaptation control signal 205 b corresponds to a product of a partial weighting factor c₁(t) and the correlation factor r(t), while the second adaptation control signal 205 c corresponds to a product of the partial weighting factor c₁(t) and the complement [1−r(t)] of the correlation factor r(t). The sum signal 115a is multiplied in the multiplier 114 b by a final weighting factor c₂(t) to produce the final equalization feedback signal 115 b.

In scenario C, the first adaptation control signal 205 b corresponds to the correlation factor r(t), while the second adaptation control signal 205 c corresponds to the complement [1−r(t)] of the correlation factor r(t). The sum signal 115 a is multiplied in the output multiplier 114 b by the weighting factor c(t) to produce the final equalization feedback signal 115 b.

A number of enhancements or modifications may be used to improve the performance over the IFTA with two taps within the fat tap.

Fixed Ratio Fat Tap with Hypothesis Testing

In this modification, adaptation of r may not occur in a continuous-time basis. One tap in the fat tap may be set to be at c with LMS adaptation (discrete-time or continuous-time), while the coefficient of the other tap within the fat tap is related to the first tap coefficient as a multiple by a correlation parameter (of the form

$\frac{1 - r}{r}$ as described above). A discrete set of such hypotheses corresponding to different values of the correlation parameter

$\frac{1 - r}{r}$ may be assumed. Each hypothesis is tested and the different taps, which may be LMS-adaptable, are adapted and, after convergence, the steady-state mean square error and/or the adapted filter coefficients may be used to decide on the right hypothesis (the right hypothesis may be selected to be the one with minimum MSE and/or acceptable patterns within the tap coefficients).

Multi-tap Fat Tap with Linear Interpolation

Multiple taps (more than two) and/or a variable number of taps may be used within a fat tap. A simple but effective approach here is to do multiple stages of linear interpolation, each stage consisting of a linear interpolation between some two points obtained from the earlier stage to give one new point which may be used in the next stage. The multi-tap fat tap will then have more than two parameters to adapt.

As an example, consider three feedback taps within a fat tap with input signals s(t), s(t−τ), s(t−2·τ). Then, s(t−τ_(r) ₁ )=r₁·s(t)+(1−r₁)·s(t−τ) may first be formed as a linear interpolation of s(t),s(t−τ), and then s(t−τ_(r) ₂ )=r₂·s(t−τ_(r) ₁ )+(1−r₂)·s(t−2·τ) is expected to be the symbol-spaced feedback signal. The feedback tap coefficients for the fat tap with input signals s(t),s(t−τ), s(t−2·τ) are then c·r₁·r₂, c·(1−r₁)·r₂,c (1−r₂). The adaptation updates of the 3 parameters r₁, r₂, c in the continuous-time domain are as follows:

c(t) = μ_(c) ⋅ ∫₀^(t)e(v) ⋅ [r₁ ⋅ r₂ ⋅ s(v) + (1 − r₁) ⋅ r₂ ⋅ s(v − τ) + (1 − r₂) ⋅ s(v − 2 ⋅ τ)]𝕕v r₁(t) = μ_(r) ⋅ ∫₀^(t)c(v) ⋅ r₂(v) ⋅ e(v) ⋅ [s(v) − s(v − τ)]𝕕v r₂(t) = μ_(r) ⋅ ∫₀^(t)c(v) ⋅ e(v) ⋅ [r₁ ⋅ s(v) + (1 − r₁) ⋅ s(v − τ) − s(v − 2 ⋅ τ)]𝕕v

Knowing a priori the signs of c, r₂ the above equations may be simplified. With an intermediate output of the fat tap defined as f _(i)(t)=c·r ₁ ·r ₂ s(t)+c·(1−r ₁)·r ₂ s(t−τ), and the final output as f(t)=f _(i)(t)+c·(1−r ₂)·s(t−2·τ), then the following simplified update equations result:

$\begin{matrix} {{r_{1}(t)} = {\mu_{r} \cdot {\int_{0}^{t}{{{e(\nu)} \cdot \frac{\mathbb{d}{f_{i}(\nu)}}{\mathbb{d}\nu}}{\mathbb{d}\nu}}}}} \\ {{r_{2}(t)} = {\mu_{r} \cdot {\int_{0}^{t}{{{e(\nu)} \cdot \frac{\mathbb{d}{f(\nu)}}{\mathbb{d}\nu}}{\mathbb{d}\nu}}}}} \end{matrix}$ Note that

$\frac{\mathbb{d}{f_{i}(\nu)}}{\mathbb{d}\nu},\frac{\mathbb{d}{f(\nu)}}{\mathbb{d}\nu}$ may easily be implemented by passing the outputs of the fat tap f_(i)(t), f(t) through the C-R differentiator block, which is a high-pass filter.

Multi-tap Fat Tap with Superlinear Interpolation

More general interpolation can also be employed, especially when more than two taps are included within the fat tap, such as quadratic interpolation. For example, with three feedback taps within a fat tap and with input signals s(t),s(t−τ),s(t−2·τ), the corresponding tap coefficients may be given as c·f₀(r),c·f₁(r),c·f₂(r) for some appropriately selected functions f₀(·), f₁(·), f₂(·), which in general may also be functions of more than one parameter. The adaptation updates are then given as:

$\begin{matrix} {{c(t)} = {\mu_{c} \cdot {\int_{0}^{t}{{{e(\nu)} \cdot \left\lbrack {{{f_{0}(r)} \cdot {s(\nu)}} + {{f_{1}(r)} \cdot {s\left( {\nu - \tau} \right)}} + {{f_{2}(r)} \cdot {s\left( {\nu - {2 \cdot \tau}} \right)}}} \right\rbrack}{\mathbb{d}\nu}}}}} \\ {{\frac{\mathbb{d}}{\mathbb{d}t}{r(t)}} = {{c(t)} \cdot {e(t)} \cdot \left\lbrack {{{f_{0}^{\prime}(r)} \cdot {s(t)}} + {{f_{1}^{\prime}(r)} \cdot {s\left( {t - \tau} \right)}} + {{f_{2}^{\prime}(r)} \cdot {s\left( {t - {2 \cdot \tau}} \right)}}} \right\rbrack}} \end{matrix}$ which may be approximated by the following explicit update equation for r(t):

r(t) = μ_(r) ⋅ ∫₀^(t)c(ν) ⋅ e(ν) ⋅ [f₀^(′)(r) ⋅ s(ν) + f₁^(′)(r) ⋅ s(ν − τ) + f₂^(′)(r) ⋅ s(ν − 2 ⋅ τ)]𝕕ν

Fat Tap With Gain Offset

To compensate for a residual but unknown gain offset between the taps in a fat tap or to control the linearity range, a fat tap with gain offset may be used. For example, consider two feedback taps within a fat tap with input signals s(t),s(t−τ). The tap coefficients for these two taps are then respectively c·r, c·a (1−r). The adaptation updates for the three parameters (c,a,r ) are then given as:

$\begin{matrix} {{c(t)} = {\mu_{c} \cdot {\int_{0}^{t}{{{e(\nu)} \cdot \left\lbrack {{r \cdot {s(\nu)}} + {a \cdot \left( {1 - r} \right) \cdot {s\left( {\nu - \tau} \right)}}} \right\rbrack}{\mathbb{d}\nu}}}}} \\ {{r(t)} = {\mu_{r} \cdot {\int_{0}^{t}{{{c(\nu)} \cdot {e(v)} \cdot \left\lbrack {{s(\nu)} - {a \cdot {s\left( {\nu - \tau} \right)}}} \right\rbrack}{\mathbb{d}\nu}}}}} \\ {{a(t)} = {\mu_{c} \cdot {\int_{0}^{t}{{{c(\nu)} \cdot {e(\nu)} \cdot \left( {1 - r} \right) \cdot {s\left( {\nu - \tau} \right)}}{\mathbb{d}\nu}}}}} \end{matrix}$

Correlated Fat Tap Adaptation (CFTA)

Multiple fat taps may share one or more taps such that each tap could correspond to more than one symbol (e.g., two symbols). It would then be expected that a set of fat taps together emulate multiple symbol-spaced feedback taps. For example, consider three feedback taps with input signals s(t),s(t−τ), s(t−2·τ) such that these together could correspond to two symbol-spaced feedback taps. The first fat tap which corresponds to the first past symbol consists of the feedback taps with inputs s(t),s(t−τ), and the second fat tap corresponds to the second past symbol and consists of the feedback taps with inputs s(t−τ),s(t−2·τ); thus, the fat taps have an overlapping feedback tap. The feedback tap coefficients may then be expressed as c₁ ·r ₁ ,c ₁·(1−r ₁)+c ₂ ·r ₂ ,c ₂·(1−r ₂). The update equations for c₁,c₂,r₁,r₂ are similarly expressed as follows:

$\begin{matrix} {{c_{1}(t)} = {\mu_{c} \cdot {\int_{0}^{t}{{{e(\nu)} \cdot \left\lbrack {{r_{1} \cdot {s(\nu)}} + {\left( {1 - r_{1}} \right) \cdot {s\left( {\nu - \tau} \right)}}} \right\rbrack}{\mathbb{d}\nu}}}}} \\ {{r_{1}(t)} = {\mu_{r} \cdot {\int_{0}^{t}{{{c_{1}(\nu)} \cdot {e(v)} \cdot \left\lbrack {{s(\nu)} - {s\left( {\nu - \tau} \right)}} \right\rbrack}{\mathbb{d}\nu}}}}} \\ {{c_{2}(t)} = {\mu_{c} \cdot {\int_{0}^{t}{{{e(\nu)} \cdot \left\lbrack {{r_{2} \cdot {s(\nu)}} + {\left( {1 - r_{2}} \right) \cdot {s\left( {\nu - \tau} \right)}}} \right\rbrack}{\mathbb{d}\nu}}}}} \\ {{r_{2}(t)} = {\mu_{r} \cdot {\int_{0}^{t}{{{c_{2}(\nu)} \cdot {e(v)} \cdot \left\lbrack {{s(\nu)} - {s\left( {\nu - \tau} \right)}} \right\rbrack}{{\mathbb{d}\nu}.}}}}} \end{matrix}$

Quasi-LMSE-based Adaptation Schemes for Fat Tap Interpolating Mixer

Other adaptation techniques for controlling the timing control ratio parameter in the interpolating mixer within the Fat Tap may also be used. One such technique may include the use of tap coefficients on the feedforward/feedback equalizers which adapt based on LMSE, in a manner that this approximates LMSE-based adaptation for the timing control ratio parameter. Thus, if the feedforward tap coefficients within the Fat Tap are of the form {c_(i)}_(i=0) ^(L), two alternative manners of adapting the timing control ratio are provided below:

$r = {\mu \cdot {\int_{0}^{t}{\left( {\sum\limits_{i = 0}^{L}{w_{i} \cdot c_{i}}} \right){\mathbb{d}t}}}}$ or alternatively

$r = {\mu \cdot {\int_{0}^{t}{\left( {\sum\limits_{i = 0}^{L}{\sum\limits_{j = 0}^{L}{w_{i,j} \cdot c_{i} \cdot c_{j}}}} \right){\mathbb{d}t}}}}$ for appropriately selected adaptation parameter: μ and real number weights {w_(i)}_(i=0) ^(L) or

{w_(i, j)}_(i, j = 0)^(i, j = L).

Referring to FIG. 10, another embodiment 200 c of the FTA circuitry 200 (FIG. 2) uses alternative implementations 204 b, 206 c of the control signal generators to process the incoming time-delayed data signals 111 a, 111 b, the error signal 117 and adaptive filter coefficient signals 15 (discussed in more detail below) from the feedforward filter 102 a of the equalizer 100 (FIG. 1).

Referring to FIG. 11, the feedforward filter 102 a processes the incoming data signal 101 to produce the equalized signal 109 using a series of signal delay elements 32 a, 32 b, . . . , 32 n, multiplier circuits 34 a, 34 b, . . . , 34 n and output summing circuit 108 a in accordance with well-known techniques. Each of the successively delayed versions 33 a, 33 b, . . . , 33 n of the data signal, as well as the incoming data signal 101, is multiplied in one of the multiplication circuits 34 a, 34 b, . . . , 34 n with its respective adaptive filter coefficient signal 15 a, 15 b, . . . , 15 n (along with a multiplication, or scaling, constant, as desired). The resulting product signals 35 a, 35 b, . . . , 35 n are summed in the signal summing circuit 108 a, with the resulting sum signal forming the equalized signal 109.

Referring to FIG. 12, an adaptive coefficients generator 14 processes the incoming data signal 101 and the error signal 117 using series of signal delay elements 42 a, 42 b, . . . , 42 n, signal multipliers 44 a, 44 b, . . . , 44 n and signal integrators (e.g., low pass filters) 46 a, 46 b, . . . , 46 n in accordance with well known techniques. The incoming signal 101 is successively delayed by the signal delay elements 42 a, 42 b, . . . , 42 n to produce successively delayed versions 43 a, 43 b, . . . , 43 n of the incoming signal 101. Each of these signals 101, 43 a, 43 b, . . . , 43 n is multiplied in its respective signal multiplier 44 a, 44 b, . . . , 44 n with the error signal 117 (along with a multiplication, or scaling, constant, as desired). The resulting product signals 45 a, 45 b, . . . , 45 n are individually integrated in the signal integration circuits 46 a, 46 b, . . . , 46 n to produce the individual adaptive filter coefficient signals 15 a, 15 b, . . . , 15 n.

Referring to FIG. 13, one embodiment 206 ca of this alternative second control signal generator in accordance with the presently claimed invention includes a set of signal weighting circuits (e.g., multipliers) 156 a, 156 b, . . . , 156 n, a signal combining (e.g., summing) circuit 158 and a signal integration circuit (e.g., low pass filter) 160, interconnected substantially as shown. Each of the adaptive filter coefficient signals 15 a, 15 b, . . . , 15 n is weighted (e.g., multiplied) in a respective multiplier 156 a, 156 b . . . , 156 n with a corresponding weighted, or scaled, signal 155 a, 155 b, . . . , 155 n (as well as a multiplication, or scaling, factor μ 161, as desired). The resulting product signals 157 a, 157 b, . . . 157 n are combined (e.g., summed) in the signal combiner 158. The combined signal 159 is integrated (e.g., low pass filtered) by the signal integrator 160 to produce the adaptation control signal 207 ac r(t). This signal 207 ac is also complemented by signal complement circuitry 228 (as discussed above) to produce the other adaptation control signal 207 bc [1−r(t)] provided to the first control signal generator 204 b.

Referring to FIG. 14, another embodiment 206 cb of the second control signal generator 206 c in accordance with the presently claimed invention includes an alternative implementation 164 of weighting circuitry for weighting the adaptive filter coefficient signals 15 with corresponding weighted, or scaled, signals 155 (as well as a multiplication, or scaling, factor μ 161, as desired). Such weighting circuitry 164 can be implemented in accordance with well-known techniques using multiple signal weighting circuits (e.g., multipliers) and signal combining (e.g., summing) circuits to perform the prescribed weighting of the respective adaptive filter coefficient signals 15 with the corresponding weighted, or scaled, signals 155 over the appropriate ranges of i and j. As before, the resultant signal 165 is integrated (e.g., low pass filtered) by a signal integrator 160 to produce the adaptation control signal 207 ad r(t). This signal 207 ad is also complemented by signal complement circuitry 228 (as discussed above) to produce the other adaptation control signal 207 bd [1−r(t)] provided to the first control signal generator 204 b.

Alternatively, it should be understood that this technique can also be implemented using adaptive coefficient signals from an adaptive feedback filter 104 (FIG. 1).

Referring to FIG. 15, one implementation 200 ac of the FTA circuit 200 c of FIG. 10 can be implemented substantially as shown. Using the adaptation control signals 207 a, 207 b from the second control signal generator 206 c (e.g., FIG. 13 or 14), the first control signal generator 204 ba operates as discussed above in connection with FIG. 6.

Yet another technique for adapting the timing control ratio parameter may be using the “eye monitor” test.

Referring to FIGS. 16A and 16B, expected performance improvement with use of an analog continuous-time feedforward filter in conjunction with “fat tap” adaptation in accordance with the presently claimed invention is as illustrated. FIG. 16A illustrates the “eye” diagram for the incoming data signal 101 (FIG. 11) prior to equalization, while FIG. 16B illustrates the “eye” diagram for the output signal 107 of the slicer 106 following equalization in accordance with the presently claimed invention. As shown, the uncompensated waveform of FIG. 16A has “eyes” Ea which are substantially closed, thereby producing a high BER corresponding to an eye-opening penalty approaching infinity. In contrast thereto, the compensated waveform of FIG. 16B has “eyes” Eb which are substantially open, thereby producing a low BER corresponding to an eye-opening penalty of approximately three decibels.

Based upon the foregoing discussion, it should be recognized that each of the exemplary embodiments of the presently claimed invention as depicted and discussed herein offer similar advantages without any one of such embodiments necessarily being preferred over the others. As will be readily appreciated by one of ordinary skill in the art, the particular topology of each embodiment may cause one particular embodiment to be deemed more advantageous for the specific host system or network in which such embodiment is to be implemented (e.g., due to circuit design rules or layout constraints).

Various other modifications and alternations in the structure and method of operation of this invention will be apparent to those skilled in the art without departing from the scope and the spirit of the invention. Although the invention has been described in connection with specific preferred embodiments, it should be understood that the invention as claimed should not be unduly limited to such specific embodiments. It is intended that the following claims define the scope of the present invention and that structures and methods within the scope of these claims and their equivalents be covered thereby. 

1. An apparatus including fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising: a first signal terminal that conveys a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith; a second signal terminal that conveys a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period; fractional delay circuitry, coupled between said first and second signal terminals, that receives and delays said first data signal to provide said second data signal; signal weighting circuitry, coupled to said first and second signal terminals, that receives first and second weighting signals and in response thereto receives and weights said first and second data signals to provide first and second weighted signals; and signal combining circuitry, coupled to said signal weighting circuitry, that receives and combines said first and second weighted signals to provide an equalization feedback signal; wherein said first weighting signal corresponds to a product of a selected weighting factor and a correlation factor, and said second weighting signal corresponds to a product of said selected weighting factor and a difference between a normalized factor and said correlation factor.
 2. An apparatus including fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising: a first signal terminal that conveys a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith; a second signal terminal that conveys a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period; fractional delay circuitry, coupled between said first and second signal terminals, that receives and delays said first data signal to provide said second data signal; first signal weighting circuitry, coupled to said first and second signal terminals, that receives first and second weighting signals and in response thereto receives and weights said first and second data signals to provide first and second weighted signals; signal combining circuitry, coupled to said first signal weighting circuitry, that receives and combines said first and second weighted signals to provide a combined signal; and second signal weighting circuitry, coupled to said signal combining circuitry, that receives a third weighting signal and in response thereto receives and weights said combined signal to provide an equalization feedback signal; wherein said first weighting signal corresponds to a product of a first weighting factor and a correlation factor, said second weighting signal corresponds to a product of said first weighting factor and a difference between a normalized factor and said correlation factor, and said third weighting signal corresponds to a second weighting factor.
 3. The apparatus of claim 2, wherein said first weighting factor comprises unity.
 4. The apparatus of claim 2, wherein said second weighting factor comprises unity.
 5. An apparatus including fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising: fractional delay means for receiving and delaying a first data signal to generate a second data signal, wherein said first data signal corresponds to a post-slicer data signal and has a data symbol period associated therewith, and said second data signal corresponds to said first data signal delayed by a fraction of said data symbol period; signal weighting means for receiving first and second weighting signals and in response thereto weighting said first and second data signals to generate first and second weighted signals; and signal combiner means for combining said first and second weighted signals to generate an equalization feedback signal; wherein said first weighting signal corresponds to a product of a selected weighting factor and a correlation factor, and said second weighting signal corresponds to a product of said selected weighting factor and a difference between a normalized factor and said correlation factor.
 6. An apparatus including fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising: fractional delay means for receiving and delaying a first data signal to generate a second data signal, wherein said first data signal corresponds to a post-slicer slicer data signal and has a data symbol period associated therewith, and said second data signal corresponds to said first data signal delayed by a fraction of said data symbol period; first signal weighting means for receiving first and second weighting signals and in response thereto weighting said first and second data signals to generate first and second weighted signals; signal combiner means for combining said first and second weighted signals to generate a combined signal; and second signal weighting means for receiving a third weighting signal and in response thereto weighting said combined signal to generate an equalization feedback signal; wherein said first weighting signal corresponds to a product of a first weighting factor and a correlation factor, said second weighting signal corresponds to a product of said first weighting factor and a difference between a normalized factor and said correlation factor, and said third weighting signal corresponds to a second weighting factor.
 7. A method for providing fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide post-slicer data signal, comprising: receiving a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith; delaying said first data signal to generate a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period; receiving first and second signals and in response thereto weighting said first and second data signals to generate first and second weighted signals by receiving a first signal corresponding to a product of a selected weighting factor and a correlation factor, and receiving a second weighting signal corresponding to a product of said selected weighting factor and a difference between a normalized factor and said correlation factor; and combining said first and second weighted signals to generate an equalization feedback signal.
 8. A method for providing fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising: receiving a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith; delaying said first data signal to generate a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period; receiving first and second weighting signals and in response thereto weighting said first and second data signals to generate first and second weighted signals by receiving a first signal corresponding to a product of a first weighting factor and a correlation factor, receiving a second weighting signal corresponding to a product of said first weighting factor and a difference between a normalized factor and said correlation factor, and receiving a third weighting signal corresponding to a second weighting factor; combining said first and second weighted signals to generate a combined signal; and receiving a third weighting signal and in response thereto weighting said combined signal to generate an equalization feedback signal.
 9. The method of claim 8, wherein said receiving a first weighting signal corresponding to a product of a first weighting factor and a correlation factor comprises receiving a first weighting signal corresponding to a product of unity and said correlation factor.
 10. The method of claim 8, wherein said receiving a third weighting signal corresponding to a second weighting factor comprises receiving a third weighting signal corresponding to unity.
 11. An apparatus including an adaptive feedback coefficient signal generator for use in an adaptive signal equalizer with an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, with fractionally-spaced feedback and in which an equalization feedback signal adaptively equalized an incoming data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising: first signal multiplication circuitry that receives and multiplies a plurality of multiplicand signals to provide a plurality of product signals, wherein said plurality of multiplicand signals comprises a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith, a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period, an error signal corresponding to a difference between said post-slicer data signal and a pre-slicer data signal, a first adaptation control signal having a first value bounded by lower and upper value, and a second adaptation control signal having a second value related to a difference between a normalized value and said first value, and said plurality of product signals comprises a first product signal corresponding to a product of said first data signal, said error signal and said first adaptation control signal, and a second product signal corresponding to a product of said second data signal, said error signal and said second adaptation control signal; first signal combining circuitry, coupled to said first signal multiplication circuitry, that receives and combines said plurality of product signals to provide a first combined signal; first signal integration circuitry, coupled to said first signal combining circuitry, that receives and integrates said first combined signal to provide a third adaptation control signal; second signal circuitry, coupled to said first signal integration circuitry, that receives and multiplies said first, second and third adaptation control signals to provide a plurality of adaptive feedback coefficient signals; signal weighting circuitry, coupled to said first signal multiplication circuitry and said second signal multiplication circuitry, that receives a plurality of weighted coefficient signals and in response thereto receives and weights a plurality of adaptive filter coefficient signals to provide said first adaptation control signal; and signal complement circuitry coupled to said first signal multiplication circuitry, said second signal multiplication circuitry and said signal weighting circuitry, that receives and complements said first adaptation control signal to provide said second adaptation control signal.
 12. The apparatus of claim 11, further comprising: fractionally-spaced feedback circuitry, coupled to said first signal multiplication circuitry, that receives said post-slicer data signal and in response thereto provides said first and second data signals; third signal multiplication circuitry, coupled to said fractionally-spaced feedback circuitry and said second signal multiplication circuitry, that receives and multiplies said first and second data signals and said plurality of adaptive feedback coefficient signals to provide a plurality of adaptive feedback signals; and second signal combining circuitry, coupled to said third signal multiplication circuitry, that receives and combines said plurality of adaptive feedback signals to provide said equalization feedback signal; wherein said second data signal is caused to appear delayed by a time interval substantially equal to said data symbol period such that said fractionally-spaced feedback circuitry emulates symbol-spaced feedback circuitry.
 13. The apparatus of claim 11, wherein said first signal combining circuitry comprises signal summing circuitry that sums said plurality of product signals to provide a sum signal as said first combined signal.
 14. The apparatus of claim 11, wherein said first signal integration circuitry comprises low pass filter circuitry that low pass filters said first combined signal to provide a low pass filtered signal as said third adaptation control signal.
 15. The apparatus of claim 11, wherein said signal weighting circuitry comprises: third signal multiplication circuitry that receives and selectively multiplies said plurality of weighted coefficient signals and said plurality of adaptive filter coefficient signals to provide a plurality of weighted signals; second signal combining circuitry, coupled to said third signal multiplication circuitry, that receives and combines said plurality of weighted signals to provide a second combined signal; and second signal integration circuitry, coupled to said second signal combining circuitry, that receives and integrates said second combined signal to provide said first adaptation control signal.
 16. The apparatus of claim 15, wherein said second signal integration circuitry comprises low pass filter circuitry that low pass filters said second combined signal to provide a low pass filtered signal as said first adaptation control signal.
 17. The apparatus of claim 11, wherein said signal complement circuitry comprises signal subtraction circuitry that subtracts said first adaptation control signal from a reference signal having said normalized value to provide a difference signal as said second adaptation control signal.
 18. An apparatus including an adaptive feedback coefficient signal generator for use in an adaptive signal equalizer with an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, with fractionally-spaced feedback and in which an equalization feedback signal adaptively equalizes an incoming data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising: first control signal generator circuitry that receives and processes a plurality of input signals and first and second adaptation control signals and in response thereto provides a plurality of adaptive feedback coefficient signals, wherein said plurality of input signals comprises a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith, a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period, and an error signal corresponding to a difference between said post-slicer data signal and a pre-slicer data signal; and second control signal generator circuitry, coupled to said first control signal generator circuitry, that receives and processes a plurality of adaptive filter coefficient signals and in response thereto provides said first and second adaptation control signals.
 19. The apparatus of claim 18, further comprising: fractionally-spaced feedback circuitry that receives said post-slicer data signal and in response thereto provides said first and second data signals; signal multiplication circuitry, coupled to said fractionally-spaced feedback circuitry and said first control signal generator circuitry, that receives and multiplies said first and second data signals and said plurality of adaptive feedback coefficient signals to provide a plurality of adaptive feedback signals; and signal combining circuitry, coupled to said signal multiplication circuitry, that receives and combines said plurality of adaptive feedback signals to provide said equalization feedback signal; wherein said second data signal is caused to appear delayed by a time interval substantially equal to said data symbol period such that said fractionally-spaced feedback circuitry emulates symbol-spaced feedback circuitry.
 20. The apparatus of claim 18, wherein: said first adaptation control signal has a first value bounded by lower and upper values; and said second adaptation control signal has a second value related to a difference between a normalized value and said first value.
 21. The apparatus of claim 18, wherein said first control signal generator circuitry comprises: first signal multiplication circuitry that receives and multiplies said plurality of input signals and said first and second adaptation control signals to provide a plurality of product signals comprising a first product signal corresponding to a product of said first data signal, said error signal and said adaptation control signal, and a second product signal corresponding to a product of said second data signal, said error signal and said second adaptation control signal; signal combining circuitry, coupled to said signal multiplication circuitry, that receives and combines said plurality of product signals to provide a combined signal; signal integration circuitry, coupled to said signal combining circuitry, that receives and integrates said combined signal to provide said third adaptation control signal; and second signal multiplication circuitry, coupled to said signal integration circuitry, that receives and multiplies said first, second and third adaptation control signals to provide said plurality of adaptive feedback coefficient signals.
 22. The apparatus of claim 21, wherein said signal combining circuitry comprises signal summing circuitry that sums said plurality of product signals to provide a sum signal as said combined signal.
 23. The apparatus of claim 21, wherein said signal integration circuitry comprises low pass filter circuitry that low pass filters said combined signal to provide a low pass filtered signal as said third adaptation control signal.
 24. The apparatus of claim 18, wherein said second control signal generator circuitry comprises: signal weighting circuitry that receives a plurality of weighted coefficient signals and in response thereto receives and weights said plurality of adaptive filter coefficient signals to provide said first adaptation control signal; and signal complement circuitry, coupled to said signal weighting circuitry, that receives and complements said first adaptation control signal to provide said second adaptation control signal.
 25. The apparatus of claim 24, wherein said signal weighting circuitry comprises: signal multiplication circuitry that receives and selectively multiplies said plurality of weighted coefficient signals and said plurality of adaptive filter coefficient signals to provide a plurality of product signals; signal combining circuitry, coupled to said signal multiplication circuitry, that receives and combines said plurality of product signals to provide a combined signal; and signal integration circuitry coupled to said signal combining circuitry, that receives and integrates said combined signal to provide said first adaptation control signal.
 26. The apparatus of claim 25, wherein said signal integration circuitry comprises low pass filter circuitry that low pass filters said combined signal to provide a low pass filtered signal as said first adaptation control signal.
 27. The apparatus of claim 24, wherein said signal complement circuitry comprises signal subtraction circuitry that subtracts said first adaptation control signal from a reference signal having a normalized value to provide a difference signal as said second adaptation control signal.
 28. An apparatus including an adaptive feedback coefficient signal generator for use in an adaptive signal equalizer with an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, with fractionally-spaced feedback and in which an equalization feedback signal adaptively equalizes an incoming data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising: first multiplier means for receiving and multiplying a plurality of multiplicand signals and providing plurality of product signals, wherein said plurality of multiplicand signals comprises a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith, a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period, an error signal corresponding to a difference between said post-slicer data signal and a pre-slicer data signal, a first adaptation control signal having a first value bounded by lower and upper values, and a second adaptation control signal having a second value related to a difference between a normalized value and said first value, and said plurality of product signals comprises a first product signal corresponding to a product of said first data signal, said error signal and said first adaptation control signal, and a second product signal corresponding to a product of said second data signal, said error signal and said second adaptation control signal; first combiner means for combining said plurality of product signals and providing a first combined signal; signal integrator means for integrating said first combined signal and providing a third adaptation control signal; second multiplier means for multiplying said first, second and third adaptation control signals and providing a plurality of adaptive feedback coefficient signals; weighting means for receiving a plurality of weighted coefficient signals and in response thereto receiving and weighting a plurality of adaptive filter coefficient signals and providing said first adaptation control signal; and complement means for complementing said first adaptation control signal and providing said second adaptation control signal.
 29. The apparatus of claim 28, further comprising: feedback means for delaying said post-slicer data signal in a successively fractionally-spaced manner and providing said first and second data signals; third multiplier means for multiplying said first and second data signals and said plurality of adaptive feedback coefficient signals and providing a plurality of adaptive feedback signals; and second combiner means for combining said plurality of adaptive feedback signals and providing said equalization feedback signal; wherein said second data signal is caused to appear delayed by a time interval substantially equal to said data symbol period such that said fractionally-spaced feedback circuitry emulates symbol-spaced feedback circuitry.
 30. An apparatus including an adaptive feedback coefficient signal generator for use in an adaptive signal equalizer with an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, with fractionally-spaced feedback and in which an equalization feedback signal adaptively equalizes an incoming data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising: first controller means for receiving and processing a plurality of input signals and first and second adaptation control signals and providing a plurality of adaptive coefficient signals, wherein said plurality of input signals comprises a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith, a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period, and an error signal corresponding to a difference between said post-slicer data signal and a pre-slicer data signal; and second controller means for receiving and processing a plurality of adaptive filter coefficient signals and providing said first and second adaptation control signals.
 31. The apparatus of claim 30, further comprising: feedback means for delaying said post-slicer data signal in a successively fractionally-spaced manner and providing said first and second data signals; multiplier means for multiplying said first and second data signals and said plurality of adaptive feedback coefficient signals and providing a plurality of adaptive feedback signals; and combiner means for combining said plurality of adaptive feedback signals and providing said equalization feedback signal; wherein said second data signal is caused to appear delayed by a time interval substantially equal to said symbol period such that said fractionally-spaced feedback circuitry emulates symbol-spaced feedback circuitry.
 32. The apparatus of claim 30, wherein: said first adaptation control signal has a first value bounded by lower and upper values; and said second adaptation control signal has a second value related to a difference between a normalized value and said first value.
 33. The apparatus of claim 30, wherein said first controller means comprises: first multiplier means for multiplying said plurality of input signals and said first and second adaptation control signals and providing a plurality of product signals comprising a first product signal corresponding to a product of said first data signal, said error signal and said first adaptation control signal, and a second product signal corresponding to a product of said second data signal, said error signal and said second adaptation control signal; combiner means for combining said plurality of product signals and providing a combined signal; integrator means for integrating said combined signal and providing a third adaptation control signal; and second multiplier means for multiplying said first, second and third adaptation control signals and providing said plurality of adaptive feedback coefficient signals.
 34. The apparatus of claim 30, wherein said second controller means comprises: weighting means for receiving a plurality of weighted coefficient signals and in response thereto weighting said plurality of adaptive filter coefficient signals and providing said first adaptation control signal; and complement means for complementing said first adaptation control signal and providing said second adaptation control signal.
 35. A method for generating adaptive feedback coefficient signals for adaptive signal equalization using an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, fractionally-spaced feedback and an equalization feedback signal to generate an adaptively equalized data signal as a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising: receiving and multiplying a plurality of multiplicand signals to generate a plurality of product signals, wherein said plurality of multiplicand signals comprises a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith, a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period, an error signal corresponding to a difference between said post-slicer data signal and a pre-slicer data signal, a first adaptation control signal having a first value bounded by lower and upper values, and a second adaptation control signal having a second value related to a difference between a normalized value and said first value, and said plurality of product signals comprises a first product signal corresponding to a product of said first data signal, said error signal and said first adaptation control signal, and a second product signal corresponding to a product of said second data signal, said error signal and said second adaptation control signal; combining said plurality of product signals to generate a first combined signal; integrating said first combined signal to generate a third adaptation control signal; multiplying said first, second and third adaptation control signals to generate a plurality of adaptive coefficient signals; receiving a plurality of weighted coefficient signals and in response thereto receiving and weighting a plurality of adaptive filter coefficient signals to generate said first adaptation control signal; and complementing said first adaptation control signal to generate said second adaptation control signal.
 36. The method of claim 35, further comprising: delaying said post-slicer data signal in a successively fractionally-spaced manner to generate said first and second data signals; multiplying said first and second data signals and said plurality of adaptive feedback coefficient signals to generate a plurality of adaptive feedback signals; and combining said plurality of adaptive feedback signals to generate said equalization feedback signal; wherein said second data signal is caused to appear delayed by a time interval substantially equal to said data symbol period such that said delaying said post-slicer data signal in a successively fractionally-spaced manner to generate said first and second data signals emulates delaying said post-slicer data signal in a successively symbol-spaced manner to generate said first and second data signals.
 37. A method for generating adaptive feedback coefficient signals for adaptive signal equalization using an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, fractionally-spaced feedback an equalization feedback signal to generate an adaptively equalized data signal as a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising: receiving and processing a plurality of input signals and first and second adaptation control signals to generate a plurality of adaptive feedback coefficient signals, wherein said plurality of input signals comprises a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith, a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period, and an error signal corresponding to a difference between said post-slicer data signal and a pre-slicer data signal; and receiving and processing a plurality of adaptive filter coefficient signals to generate said first and second adaptation control signals.
 38. The method of claim 37, further comprising: delaying said post-slicer data signal in a successively fractionally-spaced manner to generate said first and second data signals; multiplying said first and second data signals and said plurality of adaptive feedback coefficient signals to generate a plurality of adaptive feedback signals; and combining said plurality feedback signals to generate said equalization feedback signal; wherein said second data signal is caused to appear delayed by a time interval substantially equal to said data symbol period such that said delaying said post-slicer data signal in a successively fractionally-spaced manner to generate said first and second data signals emulates delaying said post-slicer data signal in a successively symbol-spaced manner to generate said first and second data signals.
 39. The method of claim 37, wherein said receiving and processing a plurality of adaptive filter coefficient signals to generate said first and second adaptation control signals comprises: generating said first adaptation control signal with a first value bounded by lower and upper values; and generating said second adaptation control signal with a second value related to a difference between a normalized value and said first value.
 40. The method of claim 37, wherein said receiving and processing a plurality of input signals and first and second adaptation control signals to generate a plurality of adaptive feedback coefficient signals comprises: receiving and multiplying said plurality of input signals and said first and second adaptation control signals to generate a plurality of product signals comprising a first product signal corresponding to a product of said first data signal, said error signal and said first adaptation control signal, and a second product signal corresponding to a product of said second data signal, said error signal and said second adaptation control signal; combining said plurality of product signals to generate a combined signal; integrating said combined signal to generate a third adaptation control signal; and multiplying said first, second and third adaptation control signals to generate said plurality of adaptive feedback coefficient signals.
 41. The method of claim 37, wherein said receiving and processing a plurality of adaptive filter coefficient signals to generate said first and second adaptation control signals comprises: receiving a plurality of weighted coefficient signals and in response thereto weighting said plurality of adaptive filter coefficient signals to generate said first adaptation control signal; and complementing said first adaptation control signal to generate said second adaptation control signal. 